As fighting raged Sunday in the rebel stronghold of Donetsk, a Ukrainian military spokesman denied separatists' calls for a cease-fire, saying a truce would only be possible if they surrender.

"If there is this initiative, it should be carried out by practical means and not by words — by raising white flags and by putting down guns," military spokesman Andriy Lysenko said while speaking to journalists Sunday, according to Reuters. "We have not seen these practical steps yet."

In a statement released after Lysenko spoke, rebels said they still wanted a temporary cease-fire on humanitarian grounds, but remained defiant, adding, "As long as the Ukrainian army is continuing military action there can be no cease-fire," according to Reuters.

Meanwhile, conditions were deteriorating in Donetsk as Russian-backed rebels and the Ukrainian military exchanged fire Sunday. At least one person was killed and 10 wounded in shelling, while more than 10 residential buildings, a hospital and a shop were heavily damaged overnight.

"This is a real war! It's impossible to live in this city, I've been sleeping in the basement for the past week," said Inna Drobyshevskaya, a 48-year-old lawyer in Donetsk.

"We don't want Novorossiya (New Russia) for this price," she added, referring to a term used by rebels to describe the parts of eastern Ukraine seeking independence from the government in Kiev.

The developments come after a top separatist leader admitted that Ukrainian forces had surrounded Donetsk and called for a cease-fire Saturday.

"We are ready for a cease-fire in order to avert the humanitarian catastrophe growing," Alexander Zakharchenko, prime minister of the self-styled Donetsk People's Republic (DPR), said in a statement posted on a rebel website, according to the Associated Press and Agence France-Presse.

Igor Girkin, a top commander of the pro-Russia militants, also acknowledged Saturday that Donetsk was surrounded and conceded that Ukrainian troops had gotten the upper hand in eastern Ukraine after four months of fighting.

The appeal by Zakharchenko comes as Russia is pressing to send a humanitarian convoy into Ukraine to parts of the besieged eastern regions, an offer that the Ukrainian government has labeled a ploy to cover a military invasion.

Although Western countries say Moscow has assembled about 20,000 troops just across the border, Russia has denied it.

Zakharchenko — who took over as prime minister of the DPR last week — warned that rebels were determined to defend Donetsk if Ukrainian forces tried to capture the city of 1 million people. At least 300,000 of Donetsk's residents have fled.

"The fight will be for every street, for every house, for every meter of our land," Zakharchenko said.

Russian Foreign Minister Sergei Lavrov spoke with U.S. Secretary of State John Kerry on Saturday and called for "urgent measures for preventing an impending humanitarian catastrophe" in eastern Ukraine, the Foreign Ministry said in a statement. It added that Kerry "confirmed such work is being carried out with the Kiev authorities."